This is a question for EDH, which I know has few 'official' rules comparatively, but I want to know what my options are in reference to Dark Depths.

Currently, I have it in my Olivia Voldaren deck, which includes Vampire Hexmage. The combo is very obvious there, which is why it's in. But I've been wondering if the 'color identity' rules of EDH prevent me from running it(or a second, if I purchase one) in my Captain Sisay deck? I don't think it would, given that it doesn't produce out of color mana, or have a color identity itself, but I wanted to know for sure(my local meta is pretty spot on with the rules and bannings, otherwise I'd discuss this with them).

Dark Depths can be played under any Commander. It's color identity is colorless. You can use it with Captain Sisay.

903.4. The Commander variant uses color identity to determine what cards can be in a deck with a certain commander. The color identity of a card is the color or colors of any mana symbols in that card's mana cost or rules text, plus any colors defined by its characteristic-defining abilities (see rule 604.3) or color indicator (see rule 204).

Dark Depths has no mana cost, no mana symbol on its text, no CDA defining its color, and no color indicator. So, nothing to give it a color identity.

A card's color identity is determined by the mana symbols in its mana cost, any mana symbols in its text box, and any CDAs or color indicators a card has. The Depth does not have any of those, so it can be included in any commander deck. It makes a black token, but we're looking for colored mana symbols, not color words.